Rumour Spreading without the Network Alessandro Panconesi - - PowerPoint PPT Presentation

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Rumour Spreading without the Network Alessandro Panconesi - - PowerPoint PPT Presentation

Dec 25, 2023 157 likes •842 views

Rumour Spreading without the Network Alessandro Panconesi Dipartimento di Informatica Joint work with: Pawel Brach, Alessandro Epasto, Piotr Sankowski THE STARS PEOPLE The INTERNET is an observatory of

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Rumour Spreading without the Network

Alessandro Panconesi

Dipartimento di Informatica Joint work with: Pawel Brach, Alessandro Epasto, Piotr Sankowski

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THE ¡STARS ¡

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PEOPLE ¡

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The ¡INTERNET ¡is ¡an ¡observatory ¡of ¡Crowds ¡

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Digital ¡Traces ¡

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The ¡Grand ¡Challenge ¡

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The Grand Challenge

What can we reconstruct the

  • riginal diffusion

process from the huge, and yet scanty, digital traces?

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Rumour spreading, a case study

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Gossip: a very simple model

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Gossiping

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Gossiping

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Gossiping

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Gossiping

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Gossiping

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Gossiping

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Gossiping

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Gossiping Variants PUSH

Node with information sends to a random neighbour

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Gossiping Variants PUSH PULL

Node with information sends to a random neighbour Node without information asks a random neighbour

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Gossiping Variants PUSH PULL

Node with information sends to a random neighbour Node without information asks a random neighbour

PUSH-PULL

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RUMOUR SPREADING WITHOUT THE NETWORK

The problem that we want to solve

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Beyond ¡the ¡asymptoBc ¡tradiBon ¡

Can we predict the number of informed nodes at time t on the basis of the degree distribution alone?

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Beyond ¡the ¡asymptoBc ¡tradiBon ¡

Can we predict the average number of informed nodes at time t on the basis of the degree distribution alone?

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Beyond ¡the ¡asymptoBc ¡tradiBon ¡

Can we predict the average number of informed nodes at time t on the basis of the degree distribution alone for real social networks?

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The Master Plan

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The master plan

  • Develop in a rigorous way a space-

efficient simulator for a model

  • Test it with real networks
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THE MODEL

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Configuration Model D = ( )

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Configuration Model D = ( )

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Configuration Model D = ( )

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Configuration Model D = ( )

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Configuration Model D = ( )

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Configuration Model D = ( )

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Configuration Model D = ( )

Is this a good model for social networks?

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Configuration Model D = ( )

Is this a good model for social networks? No, but this is good!

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Problem ¡restatement ¡

Can we predict the average number of informed nodes at time t on the basis of the degree distribution alone for the configuration model?

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Can we predict the average number of informed nodes at time t on the basis of the degree distribution alone for the configuration model? YES, OF COURSE!

Problem ¡restatement ¡

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Naive Simulator

  • On input D = (d1,d2,…,dn), pick a

random graph G(D) from the configuration model

  • Pick a random source and simulate

rumour spreading

  • Compute averages
  • Repeat
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THE SPACE-EFFICIENT SIMULATOR

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The Efficient Simulator D = ( )

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The Efficient Simulator D = ( )

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The Efficient Simulator D = ( )

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The Efficient Simulator D = ( )

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The Efficient Simulator D = ( )

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The Efficient Simulator D = ( )

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The Efficient Simulator D = ( )

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The Efficient Simulator D = ( )

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The Efficient Simulator D = ( )

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The Efficient Simulator D = ( )

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The Efficient Simulator D = ( )

This is space-efficient because we do not need to keep the stubs, only their number

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The Efficient Simulator D = ( )

For undirected networks further optimization is possible. The resulting savings are spectacular

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Dealing with aggregates

Rank(u) = #unused stubs of node u M[i,j] = #nodes of degree j and rank j DxD matrix

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Dealing with aggregates

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Theorem

  • The Efficient Simulator is a correct

implementation of the Naïve Simulator-- they compute the same averages

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A Picture is Worth a Thousand Words

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EXPERIMENTS WITH REAL NETWORKS

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Experiments ¡with ¡real ¡networks ¡

Input: ¡the ¡degree ¡ distribuBon ¡of ¡a ¡real ¡ network ¡

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Efficient ¡simulator ¡for ¡ the ¡configuraBon ¡model ¡

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The Good..

Epinions

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The Good..

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The Bad..

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and the Ugly

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Different behaviours

  • Friendship and trust

networks: Epinions, Facebook, LiveJournal, RenRen, and Slashdot

  • Collaboration and Email

networks: AstroPh, CondMatt, DBLP and WikiTalk; EuAll and Enron

  • Non-social newtorks: Web,

Amazon

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MEASURING RANDOMNESS

Courtesy of Silvio Lattanzi

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Sudden drops

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To summarize

  • We developed a space-efficient

predictor for the configuration model

  • Surprisingly, this works quite well for

real social networks too

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Future work

  • Look for more efficient predictors, eg

systems of differential equations

  • Go beyond averages
  • Extend to other diffusion processes?
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THANKS